The Nutty Professor sells cashews for $6.20 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 44 pound mixture that sells for $5.55 per pound?

Answer 1

Let the amount (in pounds) of cashews be represented as "c".

Let the amount (in pounds) of Brazil nuts be represented as "b".

Then, because there is 44 pounds of the mixture: b + c = 44 or we can also say b = 44 - c

The total value of the cashews is 6.20c (the price per pound multiplied by the number of pounds).

And the total value of the Brazil nuts is 5.00b

So the total price of both is 6.2c + 5b

The price per pound would be (6.2c + 5b)/44

And since the price per pound is $5.55 then (6.2c + 5b)/44 = 5.55 or:

6.2c + 5b = 5.55(44)

6.2c + 5b = 244.2

Since b = 44 - c (from the first equation), then we can replace "b" with "44 - c" to get:

6.2c + 5(44 - c) = 244.2

6.2c + 220 - 5c = 244.2

1.2c = 24.2

c = 121/6 or 20 1/6 pounds

Since b + c = 44 then b + 121/6 = 44

b = 143/6 or 23 5/6 pounds